1. Field of the Invention
The present invention relates to a pattern determining method, a pattern determining apparatus, and a non-transitory computer-readable storage medium storing a program that causes a computer to execute the method.
2. Description of the Related Art
In a lithography step of manufacturing a device such as a semiconductor device, an exposure apparatus is used to form a device pattern on a substrate. The exposure apparatus includes a projection optical system. The projection optical system projects a pattern of a mask (reticle) arranged on its object plane onto a substrate. The mask is made by undergoing a step of causing a drawing apparatus to draw, on a mask blank, a pattern to be formed on the mask blank. Examples of the drawing apparatus are an electron-beam exposure apparatus that uses an electron beam as a drawing beam, and a laser drawing apparatus that uses a laser beam as a drawing beam. A mask for the manufacture of a front-end semiconductor device is often manufactured using the electron-beam exposure apparatus.
Major drawing methods of the electron-beam exposure apparatus are a raster method and a VSB (Variable-Shaped Beam) method. In the raster method, a pattern is drawn while raster-scanning the entire surface of a mask blank. In the VSB method, an electron beam having an area larger than that in the raster method is generated. The electron beam is shielded by an aperture to form a rectangular drawing shot having an area corresponding to a pattern to be drawn, and the pattern is drawn using the drawing shot. Note that the drawing shot means a region of a mask blank exposed by irradiating the mask blank with a drawing beam (electron beam) once.
There is employed a technique of adjusting a mask pattern shape using a computer. Examples of the technique are OPC (Optical Proximity Correction) and ILT (Inverse Lithography Technology). As the patterns for devices become finer, a pattern having undergone OPC or a pattern calculated by an algorithm based on ILT can become complicated because of, for example, inclusion of curved portions.
A pattern determined by calculation cannot directly be drawn on a mask blank by, for example, a VSB drawing apparatus. The pattern needs to be divided into a plurality of drawing shots or parts (mainly, rectangles). This operation is called fracturing, and software therefor is commercially available. However, when fracturing is performed for a complex pattern, the number of generated drawing shots may explosively increase, or the drawing shot size may be excessively small. The larger the number of drawing shots is, the longer the operation time of the drawing apparatus for drawing a pattern on one mask blank is, resulting in an increase in the mask cost. Additionally, the smaller the drawing shot size is, the higher is the accuracy required to control the drawing position or drawing dose (intensity) of the drawing apparatus. This results in a decrease in the yield rate of mask manufacture, and a need for a front-end drawing apparatus may emerge to improve the yield rate. For these reasons, the masks have become very expensive in recent years, posing a serious problem in the semiconductor industry.
A raster drawing apparatus can also cause errors in the beam position or intensity due to a factor (for example, a factor caused by aberration) according to the scanning position of an electron beam. In addition, the smaller the individual pattern size is, the higher is the accuracy required to control the beam position or intensity. This may lower the yield rate of masks or the throughput of mask manufacture. Hence, a complex mask pattern results in an increase in the mask cost, as a matter of course.
U.S. Patent Application Publication No. 2011/0107277 (the '277 publication) discloses a method of parameterizing a mask pattern to determine (optimize) the mask pattern into a simple shape. The '277 publication also discloses a method of parameterizing an illumination shape to optimize the illumination shape together with the mask pattern. This is an example of a technique called SMO (Source Mask Optimization). Using the method of the '277 publication provides the ability to optimize a mask pattern into a rectangular shape simpler than in OPC or ILT. The '277 publication, however, does not consider the cost when drawing a pattern using a drawing apparatus at all.
U.S. Pat. No. 6,792,592 discloses an OPC method considering the characteristics of a drawing apparatus. However, this method only executes OPC using the characteristics of a drawing apparatus as constraint conditions, and cannot determine the mask drawing condition. In addition, the method of U.S. Pat. No. 6,792,592 only executes OPC as a means for improving the accuracy of a transfer position on a wafer. Since image characteristics when a mask pattern is transferred to a water are not taken into consideration, it is difficult to regard the method as being capable of providing a reliable mask pattern.
U.S. Pat. No. 6,931,617 discloses a method of determining a layout in consideration of the mask cost. In the '617 patent, however, the cost is only considered when integrating a plurality of cell libraries (logic circuit blocks) input in advance. Hence, the method neither optimizes a mask pattern nor considers the performance of an image on a wafer.
The fracturing method as a general technique only divides an input mask pattern into a plurality of shots, and cannot optimize the mask pattern shape itself.